Finite Group Databasebeta

← D53×#3523 #28292305

Subgroups — D53×#3523 #28292305

Order 13568.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288812C211yesmaximal, characteristic, complemented
2#20288811C211yesmaximal, characteristic, complemented
3#20288810C213yesmaximal, complemented
4#20288809C213yesmaximal, complemented
5#20288808C213yesmaximal, complemented
6#20288807C216yesmaximal, complemented
7#20288806C211yesmaximal, characteristic, complemented
8#20288805C212yesmaximal, complemented
9#20288804C216yesmaximal, complemented
10#20288803C213yesmaximal, complemented
11#20288802C212yesmaximal, complemented
12#557×D53C213yesmaximal, complemented
13#557×D53C211yesmaximal, characteristic, complemented
14#556×D53C213yesmaximal, complemented
15#552×D53C216yesmaximal, complemented
16D4×Q8×D53C212yesmaximal, complemented
17D4×Q8×D53C211yesmaximal, characteristic, complemented
18#541×D53C216yesmaximal, complemented
19#533×D53C213yesmaximal, complemented
20#529×D53C213yesmaximal
21#519×D53C212yesmaximal, complemented
22C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
23C53×#3523C211yesmaximal, characteristic, complemented
24C22×Q8×D53C2211yescharacteristic
25C22×Q8×D53C2212yes—
26#16811352C2211yescharacteristic, complemented
27#16811352C2213yescomplemented
28#16811351C2216yescomplemented
29#16811351C2213yescomplemented
30#16811351C2213yescomplemented
31#16811350C22112yescomplemented
32#16811350C2216yescomplemented
33#16811350C2216yescomplemented
34#16811349C2212yescomplemented
35#16811349C2216yescomplemented
36#16811348C2216yescomplemented
37#16811348C2213yescomplemented
38#16811348C2213yescomplemented
39#16811347C2213yescomplemented
40#16811346C2213yescomplemented
41#16811345C2216yescomplemented
42#16811344C2216yescomplemented
43#16811343C2213yescomplemented
44#16811342C2216yescomplemented
45#16811341C2216yescomplemented
46#16811340C22112yescomplemented
47#16811315C2216yescomplemented
48#16811314C2216yescomplemented
49#16811313C2216yescomplemented
50#16811312C2216yescomplemented
51#16811311C2216yescomplemented
52#16811310C22112yescomplemented
53#16811309C22112yescomplemented
54#16811308C2216yescomplemented
55#16811307C2216yescomplemented
56#16811306C22112yescomplemented
57#16811305C22112yescomplemented
58Q8×D212C2212yescomplemented
59Q8×D212C2211yescharacteristic, complemented
60D4×Dic106C2216yescomplemented
61D4×Dic106C2213yescomplemented
62#16811288C2213yescomplemented
63#16811288C2216yescomplemented
64Q8×C22⋊D53C2212yescomplemented
65Q8×C22⋊D53C2212yescomplemented
66Q8×C22⋊D53C2212yescomplemented
67#16811286C2216yescomplemented
68#16811286C2216yescomplemented
69#16811286C2216yescomplemented
70#16811236C2216yescomplemented
71#16811235C2216yescomplemented
72#16811234C2216yescomplemented
73#16811233C2216yescomplemented
74#16811233C2216yescomplemented
75#16811232C22112yescomplemented
76#16811232C22112yescomplemented
77#16811231C2216yescomplemented
78#16811231C2216yescomplemented
79#16811230C22112yescomplemented
80#16811230C22112yescomplemented
81#16811180C2213yescomplemented
82#16811179C2216yescomplemented
83#16811178C2213yescomplemented
84#16811178C2213yescomplemented
85#16811177C2216yescomplemented
86#16811177C2216yescomplemented
87#16811176C2216yescomplemented
88#16811175C2216yescomplemented
89#16811175C2216yescomplemented
90C4⋊Q8×D53C2213yes—
91C4⋊Q8×D53C2213yes—
92C4⋊Q8×D53C2216yes—
93#16811160C2213yes—
94#16811159C2213yes—
95#16811158C2213yes—
96#16811157C2213yes—
97#16811156C2216yes—
98#16811155C2213yes—
99#16811154C2213yes—
100#16811153C2216yes—
101#16811152C2213yes—
102#16811151C2216yes—
103#16811150C2216yes—
104#126×D53C22112yes—
105#126×D53C2216yes—
106#125×D53C2216yes—
107#125×D53C2213yes—
108#125×D53C22112yes—
109#125×D53C2216yes—
110#124×D53C2213yes—
111#123×D53C2216yes—
112C22⋊Q8×D53C2213yes—
113C22⋊Q8×D53C2216yes—
114C22⋊Q8×D53C2216yes—
115C22⋊Q8×D53C2216yes—
116#121×D53C2211yescharacteristic
117#16811101C2212yescomplemented
118#16811100C2216yescomplemented
119#16811100C2216yescomplemented
120#16811099C2212yescomplemented
121#16811099C2216yescomplemented
122#16811099C2216yescomplemented
123#16811099C2212yescomplemented
124C2×Q8×Dic53C2211yescharacteristic, complemented
125C2×C4×Dic106C2213yescomplemented
126C2×#13133182C2213yescomplemented
127C4×Q8×D53C2216yes—
128C4×Q8×D53C2216yes—
129C4×Q8×D53C2213yes—
130C4×Q8×D53C2213yes—
131C4×Q8×D53C2211yescharacteristic
132C4×Q8×D53C2212yes—
133C4×Q8×D53C2216yes—
134C4×Q8×D53C2213yes—
135C4×Q8×D53C2211yescharacteristic
136C4×Q8×D53C2211yescharacteristic, complemented
137C4×Q8×D53C2211yescharacteristic, complemented
138C4×Q8×D53C2213yescomplemented
139C4×Q8×D53C2213yescomplemented
140C4×D4×D53C2213yes—
141C4×D4×D53C2216yes—
142#117×D53C2216yes—
143#117×D53C2216yes—
144#117×D53C2216yes—
145C2×C4⋊C4×D53C2213yes—
146C2×C42×D53C2213yes—
147C53×#557C2213yescomplemented
148C53×#557C2211yescharacteristic, complemented
149C53×#556C2213yescomplemented
150C53×#552C2216yescomplemented
151D4×Q8×C53C2212yescomplemented
152D4×Q8×C53C2211yescharacteristic, complemented
153C53×#541C2216yescomplemented
154C53×#533C2213yescomplemented
155C53×#529C2213yes—
156C53×#519C2212yescomplemented
157C2×C4×Q8×C53C2211yescharacteristic, complemented
158C22×Dic106C2313yes—
159C22×Dic106C2316yes—
160C2×Q8×D53—28no—
161C2×Q8×D53—216no—
162C2×Q8×D53C2313yes—
163C2×Q8×D53C2316yes—
164C2×Q8×D53C2311yescharacteristic
165C2×Q8×D53C2312yes—
166C2×Q8×D53C2313yes—
167C2×Q8×D53C2316yes—
168C2×Q8×D53C2313yes—
169C2×Q8×D53C2311yescharacteristic
170C2×D4×D53C2312yes—
171C2×D4×D53C2311yescharacteristic
172C22×C4×D53C2311yescharacteristic
173C22×C4×D53C2313yes—
174C22×C4×D53C2313yes—
175C22×C4×D53C2316yes—
176#13133217C2313yes—
177#13133217C2316yes—
178#13133217C2313yes—
179#13133216C23112yes—
180#13133216C2316yes—
181#13133216C2316yes—
182#13133216C23112yes—
183#13133216C2316yes—
184#13133216C2316yes—
185#13133215C2316yes—
186#13133215C2316yes—
187#13133215C2316yes—
188#13133215C2316yes—
189#13133212C23112yes—
190#13133212C23112yes—
191#13133212C23112yes—
192#13133212C2316yes—
193#13133212C2316yes—
194#13133212C2316yes—
195#13133211C23112yes—
196#13133211C2316yes—
197#13133210C23112yes—
198#13133210C23112yes—
199#13133210C23112yes—
200#13133210C2316yes—
201#13133210C2316yes—
202#13133210C2316yes—
203#13133209C23112yes—
204#13133209C2316yes—
205#13133209C2313yes—
206#13133209C2316yes—
207#13133208C2316yes—
208#13133208C23112yes—
209#13133208C23112yes—
210#13133208C2316yes—
211#13133208C2313yes—
212#13133208C2313yes—
213#13133208C2316yes—
214#13133208C2316yes—
215#13133207C23112yes—
216#13133207C23112yes—
217#13133207C23112yes—
218#13133207C23112yes—
219#13133207C23112yes—
220#13133207C23112yes—
221#13133207C2316yes—
222#13133207C2316yes—
223#13133207C23112yes—
224#13133207C23112yes—
225#13133206C2313yes—
226#13133205C2313yes—
227#13133204C2313yes—
228#13133203C2316yes—
229#13133203C2316yes—
230#13133202C2316yes—
231#13133202C2316yes—
232#13133201C2316yes—
233#13133200C2316yes—
234#13133199C2316yes—
235#13133199C2316yes—
236#13133198C2316yes—
237#13133197C2316yes—
238#13133197C2316yes—
239#13133197C2316yes—
240#13133197C2313yes—
241#13133196C2316yes—
242#13133196C2316yes—
243#13133196C2316yes—
244#13133196C2313yes—
245#13133195C23112yes—
246#13133195C23112yes—
247#13133195C23112yes—
248#13133195C2316yes—
249#13133194C23112yes—
250#13133194C23112yes—
251#13133194C23112yes—
252#13133194C2316yes—
253#13133193C2316yes—
254#13133193C2316yes—
255#13133193C2316yes—
256#13133193C2313yes—
257#13133192C2311yescharacteristic
258#13133191C2311yescharacteristic
259#13133190C2312yes—
260#13133189C2312yes—
261#13133188C2311yescharacteristic
262Q8×Dic53C2311yescharacteristic
263Q8×Dic53C2312yes—
264Q8×Dic53C2316yes—
265Q8×Dic53C2313yes—
266Q8×Dic53C2311yescharacteristic
267Q8×Dic53C2313yes—
268Q8×Dic53C2316yes—
269Q8×Dic53C2313yes—
270Q8×Dic53C2316yes—
271C4×Dic106C2313yes—
272C4×Dic106C2316yes—
273C4×Dic106C23112yes—
274C4×Dic106C2316yes—
275C4×Dic106C23112yes—
276C4×Dic106C2316yes—
277C4×Dic106C2313yes—
278C4×Dic106C2313yes—
279C4×Dic106C2316yes—
280C4×Dic106C2313yes—
281C4×Dic106C2316yes—
282C4×Dic106C2313yes—
283C4×Dic106C2316yes—
284C4×Dic106C23112yes—
285C4×Dic106C2316yes—
286#13133182C2313yes—
287#13133182C2316yes—
288#13133182C23112yes—
289#13133182C2316yes—
290#13133182C2316yes—
291#13133182C23112yes—
292#13133182C2313yes—
293#13133182C2313yes—
294#13133182C2316yes—
295#13133182C2313yes—
296#13133182C2316yes—
297#13133182C2316yes—
298#13133182C2313yes—
299#13133182C2316yes—
300#13133182C23112yes—
301C4×D212C2316yes—
302C4×D212C2313yes—
303D4×Dic53C2316yes—
304D4×Dic53C2313yes—
305#13133179C2316yes—
306#13133179C2313yes—
307C4×C22⋊D53C2316yes—
308C4×C22⋊D53C2316yes—
309C4×C22⋊D53C2316yes—
310#13133177C2316yes—
311#13133177C2316yes—
312#13133177C2316yes—
313#13133176C2316yes—
314#13133176C2316yes—
315#13133176C2316yes—
316#13133175C2316yes—
317#13133175C2316yes—
318#13133175C2316yes—
319#13133175C2316yes—
320#13133175C2316yes—
321#13133175C2316yes—
322#13133174C23112yes—
323#13133174C23112yes—
324#13133174C2316yes—
325#13133174C2316yes—
326#13133173C23112yes—
327#13133173C23112yes—
328#13133173C2316yes—
329#13133173C2316yes—
330C2×C4⋊Dic53C2313yes—
331C2×#11719919C2316yes—
332C4⋊C4×D53C2316yes—
333C4⋊C4×D53C2313yes—
334C4⋊C4×D53C2313yes—
335C4⋊C4×D53C2313yes—
336C4⋊C4×D53C2313yes—
337C4⋊C4×D53C2316yes—
338C4⋊C4×D53C2316yes—
339C4⋊C4×D53C2316yes—
340C4⋊C4×D53C2316yes—
341C4⋊C4×D53C2316yes—
342C4⋊C4×D53C2316yes—
343C4⋊C4×D53C2313yes—
344C4⋊C4×D53C2316yes—
345C4⋊C4×D53C2311yescharacteristic
346C4⋊C4×D53C23112yes—
347C4⋊C4×D53C2316yes—
348C22⋊C4×D53C2312yes—
349C22⋊C4×D53C2316yes—
350C22⋊C4×D53C2316yes—
351C22⋊C4×D53C2316yes—
352C22⋊C4×D53C2316yes—
353C2×C4×Dic53C2313yes—
354C2×C4×Dic53C2313yes—
355C2×C4×Dic53C2313yes—
356C42×D53C2313yes—
357C42×D53C2313yes—
358C42×D53C2313yes—
359C42×D53C2313yes—
360C42×D53C2313yes—
361C42×D53C2313yes—
362C42×D53C2313yes—
363C42×D53C2313yes—
364C42×D53C23112yes—
365C42×D53C2316yes—
366C22×Q8×C53C2311yescharacteristic
367C22×Q8×C53C2312yes—
368C4⋊Q8×C53C2313yes—
369C4⋊Q8×C53C2316yes—
370C4⋊Q8×C53C2313yes—
371#126×C53C2316yes—
372#126×C53C23112yes—
373#125×C53C23112yes—
374#125×C53C2313yes—
375#125×C53C2316yes—
376#125×C53C2316yes—
377#124×C53C2313yes—
378#123×C53C2316yes—
379C22⋊Q8×C53C2316yes—
380C22⋊Q8×C53C2316yes—
381C22⋊Q8×C53C2316yes—
382C22⋊Q8×C53C2313yes—
383#121×C53C2311yescharacteristic
384C4×Q8×C53C2311yescharacteristic
385C4×Q8×C53C2312yes—
386C4×Q8×C53C2311yescharacteristic
387C4×Q8×C53C2313yes—
388C4×Q8×C53C2313yes—
389C4×Q8×C53C2316yes—
390C4×Q8×C53C2316yes—
391C4×Q8×C53C2313yes—
392C4×Q8×C53C2316yes—
393C4×D4×C53C2316yes—
394C4×D4×C53C2313yes—
395#117×C53C2316yes—
396#117×C53C2316yes—
397#117×C53C2316yes—
398C2×C4⋊C4×C53C2313yes—
399C2×C42×C53C2313yes—
400C23×D53C2412yes—
401C23×D53C2411yescharacteristic
402C2×Q8×C53—24no—
403C2×Q8×C53—28no—
404C2×Q8×C53C2413yes—
405C2×Q8×C53C2413yes—
406C2×Q8×C53C2416yes—
407C2×Q8×C53C2411yescharacteristic
408C2×D4×C53C2412yes—
409C2×D4×C53C2411yescharacteristic
410C22×C4×C53C2411yescharacteristic
411C22×C4×C53C2413yes—
412C22×C4×C53C2413yes—
413C22×C4×C53C2416yes—
414C2×C22⋊D53C2412yes—
415C2×C22⋊D53C2412yes—
416C2×C22⋊D53C2412yes—
417C22×Dic53C2411yescharacteristic
418C22×Dic53C2413yes—
419C22×Dic53C2413yes—
420C22×Dic53C2416yes—
421Q8×D53—24no—
422Q8×D53—28no—
423Q8×D53—212no—
424Q8×D53—224no—
425Q8×D53—212no—
426Q8×D53—212no—
427Q8×D53—224no—
428Q8×D53#4118yes—
429D4×D53—28no—
430D4×D53—24no—
431C2×D212C2412yes—
432C2×D212C2411yescharacteristic
433C2×C4×D53—212no—
434C2×C4×D53—212no—
435C2×C4×D53—224no—
436C2×C4×D53—24no—
437C2×C4×D53C2411yescharacteristic
438C2×C4×D53C2413yes—
439C2×C4×D53C2411yescharacteristic
440C2×C4×D53C2411yescharacteristic
441C2×C4×D53C2416yes—
442C2×C4×D53C2412yes—
443C2×C4×D53C2413yes—
444C2×C4×D53C2413yes—
445C2×C4×D53C2416yes—
446C2×C4×D53C2413yes—
447C2×C4×D53C2413yes—
448C2×C4×D53C2413yes—
449C2×C4×D53C2413yes—
450C2×C4×D53C2416yes—
451C2×C4×D53C2416yes—
452C2×C4×D53C2413yes—
453C2×C4×D53C2411yescharacteristic
454C2×Dic106—212no—
455C2×Dic106—224no—
456C2×Dic106C2416yes—
457C2×Dic106C2413yes—
458C2×Dic106C24112yes—
459C2×Dic106C2416yes—
460C2×Dic106C2416yes—
461C2×Dic106C2413yes—
462C2×Dic106C2413yes—
463C4⋊C4×C53C2413yes—
464C4⋊C4×C53C2413yes—
465C4⋊C4×C53C2416yes—
466C4⋊C4×C53C2416yes—
467C4⋊C4×C53C2416yes—
468C4⋊C4×C53C2416yes—
469C4⋊C4×C53C2416yes—
470C4⋊C4×C53C2416yes—
471C4⋊C4×C53C2413yes—
472C4⋊C4×C53C2416yes—
473C4⋊C4×C53C2411yescharacteristic
474C4⋊C4×C53C24112yes—
475C4⋊C4×C53C2416yes—
476C22⋊C4×C53C2412yes—
477C22⋊C4×C53C2416yes—
478C22⋊C4×C53C2416yes—
479C22⋊C4×C53C2416yes—
480C22⋊C4×C53C2416yes—
481C42×C53C2413yes—
482C42×C53C2413yes—
483C42×C53C2413yes—
484C42×C53C2413yes—
485C42×C53C24112yes—
486C42×C53C2416yes—
487C22⋊Dic53C2412yes—
488C22⋊Dic53C2416yes—
489C22⋊Dic53C2416yes—
490C22⋊Dic53C2416yes—
491C22⋊Dic53C2416yes—
492#11719921C2412yes—
493#11719921C2412yes—
494#11719921C2416yes—
495#11719921C2416yes—
496#11719921C2416yes—
497#11719921C2416yes—
498#11719921C2416yes—
499#11719921C2416yes—
500#11719921C2416yes—
501#11719921C2416yes—
502C4⋊Dic53C2413yes—
503C4⋊Dic53C2413yes—
504C4⋊Dic53C2416yes—
505C4⋊Dic53C2416yes—
506C4⋊Dic53C2416yes—
507C4⋊Dic53C2416yes—
508C4⋊Dic53C2416yes—
509C4⋊Dic53C2416yes—
510C4⋊Dic53C2413yes—
511C4⋊Dic53C2416yes—
512C4⋊Dic53C2411yescharacteristic
513C4⋊Dic53C24112yes—
514C4⋊Dic53C2416yes—
515#11719919C2416yes—
516#11719919C2416yes—
517#11719919C2416yes—
518#11719919C2416yes—
519#11719919C2416yes—
520#11719919C24112yes—
521#11719919C2416yes—
522#11719919C2416yes—
523#11719919C2416yes—
524#11719919C24112yes—
525#11719919C24112yes—
526#11719919C2416yes—
527#11719919C2416yes—
528#11719919C2416yes—
529#11719919C2412yes—
530#11719919C24112yes—
531#11719919C24112yes—
532#11719919C2416yes—
533#11719919C2416yes—
534C4×Dic53C2413yes—
535C4×Dic53C2413yes—
536C4×Dic53C2413yes—
537C4×Dic53C2413yes—
538C4×Dic53C2413yes—
539C4×Dic53C2413yes—
540C4×Dic53C2413yes—
541C4×Dic53C2413yes—
542C4×Dic53C2413yes—
543C4×Dic53C2413yes—
544C4×Dic53C2413yes—
545C4×Dic53C2413yes—
546C4×Dic53C24112yes—
547C4×Dic53C24112yes—
548C4×Dic53C24112yes—
549C4×Dic53C2416yes—
550C4×Dic53C2416yes—
551C4×Dic53C2416yes—
552C23×C53C2512yes—
553C23×C53C2511yescharacteristic
554C22×D53—22no—
555C22×D53—22no—
556C22×D53—24no—
557C22×D53—24no—
558C22×D53—24no—
559C22×D532−1+414yes—
560C22×D53C2512yes—
561C22×D53C2511yescharacteristic
562C22×D53C2511yescharacteristic
563Q8×C53—26no—
564Q8×C53—212no—
565Q8×C53—26no—
566Q8×C53C2×#4114yes—
567D4×C53—24no—
568D4×C53—22no—
569C2×C4×C53—26no—
570C2×C4×C53—26no—
571C2×C4×C53—212no—
572C2×C4×C53—22no—
573C2×C4×C53C2513yes—
574C2×C4×C53C2516yes—
575C2×C4×C53C2516yes—
576C2×C4×C53C2511yescharacteristic
577C2×C4×C53C2513yes—
578C2×C4×C53C2513yes—
579C2×C4×C53C2512yes—
580C2×C4×C53C2513yes—
581C2×C4×C53C2511yescharacteristic
582C22⋊D53—24no—
583C22⋊D53—24no—
584C22⋊D53—24no—
585C2×Dic53—26no—
586C2×Dic53—26no—
587C2×Dic53—212no—
588C2×Dic53—22no—
589C2×Dic53C2513yes—
590C2×Dic53C2516yes—
591C2×Dic53C2516yes—
592C2×Dic53C2511yescharacteristic
593C2×Dic53C2513yes—
594C2×Dic53C2513yes—
595C2×Dic53C2512yes—
596C2×Dic53C2513yes—
597C2×Dic53C2511yescharacteristic
598D212—24no—
599D212—22no—
600C4×D53—26no—
601C4×D53—212no—
602C4×D53—26no—
603C4×D53—26no—
604C4×D53—26no—
605C4×D53—26no—
606C4×D53—22no—
607C4×D53—24no—
608C4×D53—212no—
609C4×D53—26no—
610C4×D53—212no—
611C4×D53—22no—
612C4×D53—26no—
613C4×D53—212no—
614C4×D53—22no—
615C4×D53C2×#41112yes—
616C4×D532−1+414yes—
617Dic106—26no—
618Dic106—212no—
619Dic106—26no—
620Dic106—212no—
621Dic106—224no—
622Dic106—212no—
623Dic106C2×#41112yes—
624C2×#3523—531nomaximal, Sylow
625C22×C53—21no—
626C22×C53—21no—
627C22×C53—22no—
628C22×C53—22no—
629C22×C53—22no—
630C22×C53C2×2−1+412yes—
631C22×C53C2611yescharacteristic
632C2×D53—21no—
633C2×D53—21no—
634C2×D53—28no—
635C2×D53—22no—
636C2×D53—22no—
637C2×D53—22no—
638C2×D53—48no—
639C2×D53C22×#4112yes—
640C2×D53C2×2−1+412yes—
641C2×D53C2×2−1+412yes—
642C2×D53C2×2−1+412yes—
643C4×C53—23no—
644C4×C53—26no—
645C4×C53—26no—
646C4×C53—23no—
647C4×C53—23no—
648C4×C53—21no—
649C4×C53—22no—
650C4×C53C22×#4116yes—
651C4×C53C2×2−1+412yes—
652Dic53—23no—
653Dic53—26no—
654Dic53—26no—
655Dic53—23no—
656Dic53—23no—
657Dic53—21no—
658Dic53—22no—
659Dic53C22×#4116yes—
660Dic53C2×2−1+412yes—
661#3523—533no—
662#3523—531no—
663#3523—533no—
664#3523—536no—
665#3523—532no—
666#3523—531no—
667#3523—536no—
668#3523—533no—
669#3523—533no—
670#3523—532no—
671#3523—531no—
672#3523D5311yescharacteristic, direct product factor
673C2×#557—531no—
674C2×#557—533no—
675C2×#556—533no—
676C2×#552—536no—
677C2×D4×Q8—532no—
678C2×D4×Q8—531no—
679C2×#541—536no—
680C2×#533—533no—
681C2×#529—533no—
682C2×#519—532no—
683C22×C4×Q8—531no—
684C2×C53—22no—
685C2×C53—42no—
686C2×C53C23×#4111yescharacteristic
687C2×C53C22×2−1+411yescharacteristic
688C2×C53C22×2−1+411yescharacteristic
689D53—22no—
690D53—42no—
691D53#352314yesdirect product factor
692C23×Q8—531no—
693C23×Q8—532no—
694#557—536no—
695#557—533no—
696#557—533no—
697#557—536no—
698#557—5312no—
699#557—536no—
700#557—532no—
701#557—536no—
702#557—536no—
703#557—533no—
704#557—533no—
705#557—531no—
706#557—533no—
707#557C2×D5311yescharacteristic, complemented
708#557C2×D5313yescomplemented
709#556—533no—
710#556—5312no—
711#556—536no—
712#556—536no—
713#556—536no—
714#556—533no—
715#556—533no—
716#556—536no—
717#556C2×D5313yescomplemented
718#552—5312no—
719#552—5312no—
720#552—536no—
721#552—5312no—
722#552—536no—
723#552—536no—
724#552—536no—
725#552—536no—
726#552—5312no—
727#552—536no—
728#552—536no—
729#552C2×D5316yescomplemented
730D4×Q8—532no—
731D4×Q8—532no—
732D4×Q8—532no—
733D4×Q8—536no—
734D4×Q8—533no—
735D4×Q8—536no—
736D4×Q8—536no—
737D4×Q8—536no—
738D4×Q8—532no—
739D4×Q8—531no—
740D4×Q8—536no—
741D4×Q8—533no—
742D4×Q8C2×D5312yescomplemented
743D4×Q8C2×D5311yescharacteristic, complemented
744#541—536no—
745#541—5312no—
746#541—5312no—
747#541—5312no—
748#541—5312no—
749#541—536no—
750#541—536no—
751#541—536no—
752#541—536no—
753#541—536no—
754#541—536no—
755#541C2×D5316yescomplemented
756#533—533no—
757#533—533no—
758#533—536no—
759#533—536no—
760#533—536no—
761#533—536no—
762#533—536no—
763#533—536no—
764#533—533no—
765#533C2×D5313yescomplemented
766C2×C4⋊Q8—533no—
767C2×C4⋊Q8—533no—
768C2×C4⋊Q8—536no—
769#529—536no—
770#529—533no—
771#529—533no—
772#529—536no—
773#529—533no—
774#529—533no—
775#529—533no—
776#529—536no—
777#529—533no—
778#529—536no—
779#529—533no—
780#529C2×D5313yes—
781C2×#126—536no—
782C2×#126—5312no—
783C2×#125—533no—
784C2×#125—536no—
785C2×#125—5312no—
786C2×#125—536no—
787C2×#124—533no—
788C2×#123—536no—
789C2×C22⋊Q8—533no—
790C2×C22⋊Q8—536no—
791C2×C22⋊Q8—536no—
792C2×C22⋊Q8—536no—
793C2×#121—531no—
794#519—532no—
795#519—536no—
796#519—536no—
797#519—532no—
798#519—532no—
799#519—536no—
800#519—536no—
801#519C2×D5312yescomplemented
802C2×C4×Q8—531no—
803C2×C4×Q8—531no—
804C2×C4×Q8—533no—
805C2×C4×Q8—531no—
806C2×C4×Q8—533no—
807C2×C4×Q8—536no—
808C2×C4×Q8—532no—
809C2×C4×Q8—536no—
810C2×C4×Q8—533no—
811C2×C4×Q8—536no—
812C2×C4×Q8—531no—
813C2×C4×Q8—533no—
814C2×C4×Q8—531no—
815C2×C4×Q8—533no—
816C2×C4×Q8—533no—
817C2×C4×Q8—533no—
818C2×C4×Q8C2×D5311yescharacteristic, complemented
819C2×C4×D4—536no—
820C2×C4×D4—533no—
821C2×#117—536no—
822C2×#117—536no—
823C2×#117—536no—
824C22×C4⋊C4—533no—
825C22×C42—533no—
826C53C2×#352311yescharacteristic, complemented, Sylow
827C22×Q8—531no—
828C22×Q8—533no—
829C22×Q8—533no—
830C22×Q8—536no—
831C22×Q8—533no—
832C22×Q8—531no—
833C22×Q8—536no—
834C22×Q8—532no—
835C22×Q8—533no—
836C22×Q8—536no—
837C22×Q8—1068no—
838C22×Q8—10616no—
839C22×Q8C22×D5311yescharacteristic
840C22×Q8C22×D5312yes—
841C22×D4—532no—
842C22×D4—531no—
843C23×C4—533no—
844C23×C4—533no—
845C23×C4—536no—
846C23×C4—531no—
847C4⋊Q8—536no—
848C4⋊Q8—536no—
849C4⋊Q8—536no—
850C4⋊Q8—536no—
851C4⋊Q8—536no—
852C4⋊Q8—536no—
853C4⋊Q8—536no—
854C4⋊Q8—536no—
855C4⋊Q8—5312no—
856C4⋊Q8—5312no—
857C4⋊Q8—533no—
858C4⋊Q8—533no—
859C4⋊Q8—536no—
860C4⋊Q8C22×D5313yes—
861C4⋊Q8C22×D5313yes—
862C4⋊Q8C22×D5316yes—
863#126—536no—
864#126—536no—
865#126—536no—
866#126—5312no—
867#126—5312no—
868#126—5312no—
869#126—536no—
870#126—536no—
871#126—536no—
872#126—5312no—
873#126—5312no—
874#126—5312no—
875#126—536no—
876#126—5312no—
877#126C22×D5316yes—
878#126C22×D53112yes—
879#125—536no—
880#125—536no—
881#125—533no—
882#125—533no—
883#125—5312no—
884#125—5312no—
885#125—536no—
886#125—536no—
887#125—5312no—
888#125—5312no—
889#125—5312no—
890#125—5312no—
891#125—5312no—
892#125—5312no—
893#125—5312no—
894#125—5312no—
895#125—536no—
896#125—536no—
897#125—533no—
898#125—536no—
899#125—5312no—
900#125—536no—
901#125C22×D5313yes—
902#125C22×D5316yes—
903#125C22×D53112yes—
904#125C22×D5316yes—
905#124—533no—
906#124—533no—
907#124—536no—
908#124—536no—
909#124—533no—
910#124C22×D5313yes—
911#123—536no—
912#123—536no—
913#123—536no—
914#123—536no—
915#123—536no—
916#123—536no—
917#123—536no—
918#123C22×D5316yes—
919C22⋊Q8—533no—
920C22⋊Q8—536no—
921C22⋊Q8—536no—
922C22⋊Q8—536no—
923C22⋊Q8—533no—
924C22⋊Q8—536no—
925C22⋊Q8—536no—
926C22⋊Q8—536no—
927C22⋊Q8—536no—
928C22⋊Q8—533no—
929C22⋊Q8—5312no—
930C22⋊Q8—536no—
931C22⋊Q8—5312no—
932C22⋊Q8—536no—
933C22⋊Q8—5312no—
934C22⋊Q8—536no—
935C22⋊Q8—536no—
936C22⋊Q8—5312no—
937C22⋊Q8—5312no—
938C22⋊Q8—5312no—
939C22⋊Q8C22×D5313yes—
940C22⋊Q8C22×D5316yes—
941C22⋊Q8C22×D5316yes—
942C22⋊Q8C22×D5316yes—
943#121—531no—
944#121—532no—
945#121—531no—
946#121—531no—
947#121—532no—
948#121C22×D5311yescharacteristic
949C4×Q8—531no—
950C4×Q8—533no—
951C4×Q8—531no—
952C4×Q8—533no—
953C4×Q8—536no—
954C4×Q8—532no—
955C4×Q8—536no—
956C4×Q8—533no—
957C4×Q8—536no—
958C4×Q8—533no—
959C4×Q8—536no—
960C4×Q8—533no—
961C4×Q8—533no—
962C4×Q8—536no—
963C4×Q8—533no—
964C4×Q8—5312no—
965C4×Q8—536no—
966C4×Q8—536no—
967C4×Q8—5312no—
968C4×Q8—536no—
969C4×Q8—536no—
970C4×Q8—533no—
971C4×Q8—5312no—
972C4×Q8—536no—
973C4×Q8—533no—
974C4×Q8—536no—
975C4×Q8—533no—
976C4×Q8—533no—
977C4×Q8—536no—
978C4×Q8—533no—
979C4×Q8—5312no—
980C4×Q8—536no—
981C4×Q8—536no—
982C4×Q8—536no—
983C4×Q8—5312no—
984C4×Q8—536no—
985C4×Q8—533no—
986C4×Q8—5312no—
987C4×Q8—536no—
988C4×Q8C22×D5311yescharacteristic
989C4×Q8C22×D5313yes—
990C4×Q8C22×D5311yescharacteristic
991C4×Q8C22×D5313yes—
992C4×Q8C22×D5316yes—
993C4×Q8C22×D5312yes—
994C4×Q8C22×D5316yes—
995C4×Q8C22×D5313yes—
996C4×Q8C22×D5316yes—
997C4×D4—536no—
998C4×D4—533no—
999C4×D4—536no—
1000C4×D4—536no—
1001C4×D4—536no—
1002C4×D4—536no—
1003C4×D4—533no—
1004C4×D4—536no—
1005C4×D4—536no—
1006C4×D4—536no—
1007C4×D4—536no—
1008C4×D4—533no—
1009C4×D4C22×D5316yes—
1010C4×D4C22×D5313yes—
1011#117—536no—
1012#117—536no—
1013#117—536no—
1014#117—536no—
1015#117—536no—
1016#117—536no—
1017#117—536no—
1018#117—536no—
1019#117—536no—
1020#117—536no—
1021#117—536no—
1022#117—5312no—
1023#117—5312no—
1024#117—536no—
1025#117—536no—
1026#117—5312no—
1027#117—5312no—
1028#117C22×D5316yes—
1029#117C22×D5316yes—
1030#117C22×D5316yes—
1031C2×C4⋊C4—536no—
1032C2×C4⋊C4—533no—
1033C2×C4⋊C4—533no—
1034C2×C4⋊C4—533no—
1035C2×C4⋊C4—536no—
1036C2×C4⋊C4—536no—
1037C2×C4⋊C4—533no—
1038C2×C4⋊C4—533no—
1039C2×C4⋊C4—536no—
1040C2×C4⋊C4—536no—
1041C2×C4⋊C4—536no—
1042C2×C4⋊C4—536no—
1043C2×C4⋊C4—536no—
1044C2×C4⋊C4—533no—
1045C2×C4⋊C4—536no—
1046C2×C4⋊C4—531no—
1047C2×C4⋊C4—5312no—
1048C2×C4⋊C4—536no—
1049C2×C4⋊C4C22×D5313yes—
1050C2×C22⋊C4—532no—
1051C2×C22⋊C4—536no—
1052C2×C22⋊C4—536no—
1053C2×C22⋊C4—536no—
1054C2×C22⋊C4—536no—
1055C2×C42—533no—
1056C2×C42—533no—
1057C2×C42—533no—
1058C2×C42—533no—
1059C2×C42—5312no—
1060C2×C42—536no—
1061C2×C42—533no—
1062C2×C42—533no—
1063C2×C42—533no—
1064C2×C42—533no—
1065C2×C42—533no—
1066C2×C42—533no—
1067C2×C42—533no—
1068C2×C42C22×D5313yes—
1069C24—531no—
1070C24—532no—
1071C2×Q8—24no—
1072C2×Q8—28no—
1073C2×Q8—538no—
1074C2×Q8—533no—
1075C2×Q8—536no—
1076C2×Q8—533no—
1077C2×Q8—536no—
1078C2×Q8—5312no—
1079C2×Q8—533no—
1080C2×Q8—536no—
1081C2×Q8—10612no—
1082C2×Q8—10624no—
1083C2×Q8—10612no—
1084C2×Q8—10612no—
1085C2×Q8—10624no—
1086C2×Q8—10612no—
1087C2×Q8—10624no—
1088C2×Q8—1064no—
1089C2×Q8—1068no—
1090C2×Q8C23×D5313yes—
1091C2×Q8C23×D5313yes—
1092C2×Q8C23×D5316yes—
1093C2×Q8C23×D5311yescharacteristic
1094C2×D4—532no—
1095C2×D4—532no—
1096C2×D4—532no—
1097C2×D4—532no—
1098C2×D4—531no—
1099C2×D4—1064no—
1100C2×D4—1068no—
1101C2×D4C23×D5312yes—
1102C2×D4C23×D5311yescharacteristic
1103C22×C4—531no—
1104C22×C4—533no—
1105C22×C4—531no—
1106C22×C4—533no—
1107C22×C4—533no—
1108C22×C4—536no—
1109C22×C4—531no—
1110C22×C4—533no—
1111C22×C4—531no—
1112C22×C4—531no—
1113C22×C4—536no—
1114C22×C4—532no—
1115C22×C4—533no—
1116C22×C4—536no—
1117C22×C4—533no—
1118C22×C4—533no—
1119C22×C4—533no—
1120C22×C4—533no—
1121C22×C4—533no—
1122C22×C4—536no—
1123C22×C4—536no—
1124C22×C4—1064no—
1125C22×C4—10612no—
1126C22×C4—10624no—
1127C22×C4—10612no—
1128C22×C4C23×D5311yescharacteristic
1129C22×C4C23×D5313yes—
1130C22×C4C23×D5313yes—
1131C22×C4C23×D5316yes—
1132C4⋊C4—536no—
1133C4⋊C4—533no—
1134C4⋊C4—536no—
1135C4⋊C4—533no—
1136C4⋊C4—536no—
1137C4⋊C4—536no—
1138C4⋊C4—536no—
1139C4⋊C4—5312no—
1140C4⋊C4—536no—
1141C4⋊C4—536no—
1142C4⋊C4—536no—
1143C4⋊C4—536no—
1144C4⋊C4—536no—
1145C4⋊C4—536no—
1146C4⋊C4—536no—
1147C4⋊C4—5312no—
1148C4⋊C4—536no—
1149C4⋊C4—5312no—
1150C4⋊C4—536no—
1151C4⋊C4—536no—
1152C4⋊C4—533no—
1153C4⋊C4—536no—
1154C4⋊C4—536no—
1155C4⋊C4—536no—
1156C4⋊C4—532no—
1157C4⋊C4—531no—
1158C4⋊C4—5312no—
1159C4⋊C4—5312no—
1160C4⋊C4—5312no—
1161C4⋊C4—536no—
1162C4⋊C4—536no—
1163C4⋊C4—536no—
1164C4⋊C4C23×D5313yes—
1165C4⋊C4C23×D5313yes—
1166C4⋊C4C23×D5316yes—
1167C4⋊C4C23×D5316yes—
1168C4⋊C4C23×D5316yes—
1169C4⋊C4C23×D5316yes—
1170C4⋊C4C23×D5316yes—
1171C4⋊C4C23×D5316yes—
1172C4⋊C4C23×D5313yes—
1173C4⋊C4C23×D5316yes—
1174C4⋊C4C23×D5311yescharacteristic
1175C4⋊C4C23×D53112yes—
1176C4⋊C4C23×D5316yes—
1177C22⋊C4—532no—
1178C22⋊C4—536no—
1179C22⋊C4—536no—
1180C22⋊C4—536no—
1181C22⋊C4—536no—
1182C22⋊C4—532no—
1183C22⋊C4—532no—
1184C22⋊C4—536no—
1185C22⋊C4—536no—
1186C22⋊C4—536no—
1187C22⋊C4—536no—
1188C22⋊C4—536no—
1189C22⋊C4—536no—
1190C22⋊C4—536no—
1191C22⋊C4—536no—
1192C22⋊C4C23×D5312yes—
1193C22⋊C4C23×D5316yes—
1194C22⋊C4C23×D5316yes—
1195C22⋊C4C23×D5316yes—
1196C22⋊C4C23×D5316yes—
1197C42—533no—
1198C42—533no—
1199C42—533no—
1200C42—533no—
1201C42—533no—
1202C42—533no—
1203C42—533no—
1204C42—533no—
1205C42—533no—
1206C42—533no—
1207C42—533no—
1208C42—533no—
1209C42—5312no—
1210C42—5312no—
1211C42—5312no—
1212C42—536no—
1213C42—536no—
1214C42—536no—
1215C42C23×D5313yes—
1216C42C23×D5313yes—
1217C42C23×D5313yes—
1218C42C23×D5313yes—
1219C42C23×D53112yes—
1220C42C23×D5316yes—
1221C23—531no—
1222C23—534no—
1223C23—531no—
1224C23—532no—
1225C23—1062no—
1226C23—1062no—
1227C23—1064no—
1228C23—1064no—
1229C23—1064no—
1230C23C24×D5312yes—
1231C23C24×D5311yescharacteristic
1232Q8—26no—
1233Q8—212no—
1234Q8—26no—
1235Q8—5312no—
1236Q8—10612no—
1237Q8—10612no—
1238Q8—10624no—
1239Q8—1066no—
1240Q8—10612no—
1241Q8—1066no—
1242Q8#41×D5314yes—
1243D4—24no—
1244D4—22no—
1245D4—1064no—
1246D4—1064no—
1247D4—1064no—
1248D4—1064no—
1249D4—1062no—
1250C2×C4—26no—
1251C2×C4—26no—
1252C2×C4—212no—
1253C2×C4—22no—
1254C2×C4—531no—
1255C2×C4—533no—
1256C2×C4—5312no—
1257C2×C4—534no—
1258C2×C4—531no—
1259C2×C4—533no—
1260C2×C4—536no—
1261C2×C4—532no—
1262C2×C4—533no—
1263C2×C4—533no—
1264C2×C4—536no—
1265C2×C4—1062no—
1266C2×C4—1066no—
1267C2×C4—10612no—
1268C2×C4—1062no—
1269C2×C4—1066no—
1270C2×C4—1066no—
1271C2×C4—1066no—
1272C2×C4—1066no—
1273C2×C4—10612no—
1274C2×C4—1066no—
1275C2×C4—1064no—
1276C2×C4—10612no—
1277C2×C4—1062no—
1278C2×C4—1066no—
1279C2×C4—10612no—
1280C2×C4—1066no—
1281C2×C4—1066no—
1282C2×C4—10612no—
1283C2×C4—1062no—
1284C2×C4C24×D5311yescharacteristic
1285C2×C4C24×D5313yes—
1286C2×C4C24×D5316yes—
1287C2×C4C24×D5312yes—
1288C2×C4C24×D5313yes—
1289C2×C4C24×D5313yes—
1290C2×C4C24×D5316yes—
1291C2×C4C24×D5313yes—
1292C2×C4C24×D5311yescharacteristic
1293C22—21no—
1294C22—21no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—532no—
1299C22—532no—
1300C22—532no—
1301C22—532no—
1302C22—1068no—
1303C22—1061no—
1304C22—1061no—
1305C22—1062no—
1306C22—1062no—
1307C22—1062no—
1308C22—2128no—
1309C222−1+4×D5312yes—
1310C22C25×D5311yescharacteristic
1311C4—23no—
1312C4—26no—
1313C4—23no—
1314C4—23no—
1315C4—21no—
1316C4—22no—
1317C4—26no—
1318C4—536no—
1319C4—532no—
1320C4—1063no—
1321C4—1066no—
1322C4—1063no—
1323C4—1063no—
1324C4—1061no—
1325C4—1062no—
1326C4—1066no—
1327C4C2×#41×D5316yes—
1328C42−1+4×D5312yes—
1329C2—22no—
1330C2—42no—
1331C2—534no—
1332C2—1062no—
1333C2—2122no—
1334C2C22×#41×D5311yescharacteristic
1335C2C2×2−1+4×D5311yescharacteristic
1336C2C2×2−1+4×D5311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3523C2
prime radical#121×D53C22
hypercenter#3523D53
hypocenterC53C2×#3523
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3523

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20288812C2semidirect
2. #20288811C2semidirect
3. #20288810C2semidirect
4. #20288809C2semidirect
5. #20288808C2semidirect
6. #20288807C2semidirect
7. #20288806C2semidirect
8. #20288805C2semidirect
9. #20288804C2semidirect
10. #20288803C2semidirect
11. #20288802C2semidirect
12. #557×D53C2semidirect
13. #557×D53C2semidirect
14. #556×D53C2semidirect
15. #552×D53C2semidirect
16. D4×Q8×D53C2semidirect
17. D4×Q8×D53C2semidirect
18. #541×D53C2semidirect
19. #533×D53C2semidirect
21. #519×D53C2semidirect
22. C2×C4×Q8×D53C2semidirect
23. C53×#3523C2semidirect
26. #16811352C22semidirect
27. #16811352C22semidirect
28. #16811351C22semidirect
29. #16811351C22semidirect
30. #16811351C22semidirect
31. #16811350C22semidirect
32. #16811350C22semidirect
33. #16811350C22semidirect
34. #16811349C22semidirect
35. #16811349C22semidirect
36. #16811348C22semidirect
37. #16811348C22semidirect
38. #16811348C22semidirect
39. #16811347C22semidirect
40. #16811346C22semidirect
41. #16811345C22semidirect
42. #16811344C22semidirect
43. #16811343C22semidirect
44. #16811342C22semidirect
45. #16811341C22semidirect
46. #16811340C22semidirect
47. #16811315C22semidirect
48. #16811314C22semidirect
49. #16811313C22semidirect
50. #16811312C22semidirect
51. #16811311C22semidirect
52. #16811310C22semidirect
53. #16811309C22semidirect
54. #16811308C22semidirect
55. #16811307C22semidirect
56. #16811306C22semidirect
57. #16811305C22semidirect
58. Q8×D212C22semidirect
59. Q8×D212C22semidirect
60. D4×Dic106C22semidirect
61. D4×Dic106C22semidirect
62. #16811288C22semidirect
63. #16811288C22semidirect
64. Q8×C22⋊D53C22semidirect
65. Q8×C22⋊D53C22semidirect
66. Q8×C22⋊D53C22semidirect
67. #16811286C22semidirect
68. #16811286C22semidirect
69. #16811286C22semidirect
70. #16811236C22semidirect
71. #16811235C22semidirect
72. #16811234C22semidirect
73. #16811233C22semidirect
74. #16811233C22semidirect
75. #16811232C22semidirect
76. #16811232C22semidirect
77. #16811231C22semidirect
78. #16811231C22semidirect
79. #16811230C22semidirect
80. #16811230C22semidirect
81. #16811180C22semidirect
82. #16811179C22semidirect
83. #16811178C22semidirect
84. #16811178C22semidirect
85. #16811177C22semidirect
86. #16811177C22semidirect
87. #16811176C22semidirect
88. #16811175C22semidirect
89. #16811175C22semidirect
117. #16811101C22semidirect
118. #16811100C22semidirect
119. #16811100C22semidirect
120. #16811099C22semidirect
121. #16811099C22semidirect
122. #16811099C22semidirect
123. #16811099C22semidirect
124. C2×Q8×Dic53C22semidirect
125. C2×C4×Dic106C22semidirect
126. C2×#13133182C22semidirect
136. C4×Q8×D53C22semidirect
137. C4×Q8×D53C22semidirect
138. C4×Q8×D53C22semidirect
139. C4×Q8×D53C22semidirect
147. C53×#557C22semidirect
148. C53×#557C22semidirect
149. C53×#556C22semidirect
150. C53×#552C22semidirect
151. D4×Q8×C53C22semidirect
152. D4×Q8×C53C22semidirect
153. C53×#541C22semidirect
154. C53×#533C22semidirect
156. C53×#519C22semidirect
157. C2×C4×Q8×C53C22semidirect
672. #3523D53direct (N × H)
691. D53#3523direct (N × H)
707. #557C2×D53semidirect
708. #557C2×D53semidirect
717. #556C2×D53semidirect
729. #552C2×D53semidirect
742. D4×Q8C2×D53semidirect
743. D4×Q8C2×D53semidirect
755. #541C2×D53semidirect
765. #533C2×D53semidirect
801. #519C2×D53semidirect
818. C2×C4×Q8C2×D53semidirect
826. C53C2×#3523semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202888122
#202888112
#202888102
#202888092
#202888082
#202888072
#202888062
#202888052
#202888042
#202888032
#202888022
#557×D532
#556×D532
#552×D532
D4×Q8×D532
#541×D532
#533×D532
#529×D532
#519×D532
C2×C4×Q8×D532
C53×#35232
C2×#352353